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<article class="li"><h3 class="heading">
<span class="type">Item</span><span class="period">.</span>
</h3>
<p>For the odd periodic extension, we have Fourier sine series:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\hat{f}_{\text{odd}}(x)=\frac{2L}{\pi}\left[\sin\frac{\pi x}{L}-\frac{1}{2}\sin\frac{2\pi x}{L} +\frac{1}{3}\sin\frac{3\pi x}{L} -\frac{1}{4} \sin\frac{4\pi x}{L}+\cdots\right].
\end{equation*}
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